Sub-NYQUIST Multichannel Blind Deconvolution
Sub-NYQUIST Multichannel Blind Deconvolution
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DOI：
10.1109/icassp39728.2021.9413856
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发表时间：
2021-06
期刊：
影响因子：
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通讯作者：
S. Mulleti;Kiryung Lee;Yonina C. Eldar
中科院分区：
文献类型：
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作者：
S. Mulleti;Kiryung Lee;Yonina C. Eldar
考虑了一个连续时间稀疏多通道盲反卷积问题。每个通道上的信号表示为一个公共源信号的卷积，其脉冲响应给出为一个稀疏滤波器。目标是通过利用通道间的相关性，从通道输出的子奈奎斯特样本中识别这些稀疏滤波器。给出了唯一识别的充分必要条件。特别是，稀疏滤波器不应该共享一个共同的稀疏卷积因子，并且每个通道必须从至少两个不同的通道中获得2L或更多的样本。我们还证明了l -稀疏滤波器在两个通道中是唯一可识别的，只要每个通道有2L2个傅立叶测量，这可以从亚奈奎斯特样本中计算出来。此外，在通道数渐近的情况下，每个通道2L的傅里叶测量是足够的。研究结果适用于雷达、声纳、超声、地震勘探等应用中多接收机、低速率传感器的设计。
We consider a continuous-time sparse multichannel blind deconvolution problem. The signal at each channel is expressed as the convolution of a common source signal and its impulse response given as a sparse filter. The objective is to identify these sparse filters from sub-Nyquist samples of channel outputs by leveraging the correlation across channels. We present necessary and sufficient conditions for the unique identification. In particular, the sparse filters should not share a common sparse convolution factor and it is necessary to have 2L or more samples per channel from at least two distinct channels. We also show that L-sparse filters are uniquely identifiable from two channels provided that there are 2L2 Fourier measurements per channel, which can be computed from sub-Nyquist samples. Additionally, in the asymptotic of the number of channels, 2L Fourier measurements per channel are sufficient. The results are applicable to the design of multi-receiver, low-rate, sensors in applications such as radar, sonar, ultrasound, and seismic exploration.